Irrationality at the pub

My friend ordered a Paulaner. The waitress brought a Staropramen by mistake. She was about to take it away and replace it, when he offered to pay half-price for it to save the cost of throwing it away.

What decision should she make? Accept the offer and avoid the wastage, or bring a new beer and charge full price?

The considerations are surprisingly complex.

A simple one is the cost of the beer. If gross margins are low - that is, if beer costs the pub more than half of what it charges the client - it is more profitable to sell the Staropramen at half price and at least get some revenue than to throw it away. On the other hand if beer is very cheap then it's more profitable to chuck the old one and charge full price for the new glass. Note that the consideration here is the wholesale price of the Paulaner which would need to be poured, not the Staropramen which would be thrown away - that has already been poured and is a sunk cost.

Assuming that it would be profitable to sell the Star at half price, lots of other considerations start to arise. Let's start with game theory. The customer has made an offer at 50% of full price - maybe they'd be willing to pay more. Should she ask for 90% and negotiate downwards from there? What is the customer willing to pay?

Will the bar be able to resell the beer? They did in fact keep the pint to one side instead of throwing it away - and when we asked, the waitress said they would sell it to another customer if it was ordered within a couple of minutes and was still fresh - but in 5 minutes they'd toss it. But I'd be willing to bet the customer who orders it from their table gets it, not the one who orders it at the bar. As it was a Monday night, the waitress pointed out, it probably won't be resold within the five minutes and will instead be emptied out.

The reputational question for the bar is double-sided. Typically, companies don't want to be seen as soft touches in negotiation. They may be willing to throw away marginal revenues in a visible way - as in the optimal play of the ultimatum game or chicken - so people don't think it's worth negotiating in future. On the other hand, perhaps they'd like to be seen as environmentally friendly, or as being flexible and helpful to the customer. It isn't clear which of these effects dominates.

The value of labour comes in at some point. If it takes five minutes to negotiate the price and three more minutes to change the order on the till so the receipt adds up, is it worth it? She's probably paid about £6 or £7 an hour, so the cost of time would be about £1. Is the search cost of finding a mutually acceptable deal worth the profit?

Actually though, it's a bit more subtle than that. The return on her labour is of course more than its cost, otherwise the bar wouldn't be in business. So while she's negotiating, all the expensive fixed assets of the bar are being wasted. On this view, that eight minutes might cost £5.

Or maybe she doesn't care about the value of her time to the bar, only to her. She'll probably be better tipped if she strikes the deal than if she doesn't. Possibly even more than the amount of the discount - since there are two other people at the table slightly embarrassed that our friend is even asking this question, and ready to put in a couple of quid just to shut him up. Maybe it's even worthwhile for her to subsidise the half price herself in order to earn it back in tips.

Which is why there's an agency problem for the bar. Does it allow its staff the discretion to make decisions like this? The waitress claimed that she couldn't accept our deal as she isn't the manager. Probably some truth in that, but is it because of the perverse incentives presented by the principal-agent conflict - or for a more practical reason:

Cognitive load and granularity. At the volume of business done by a typical bar, it's not necessarily optimal for agents to make individual decisions. They may not have the economics training to take into account all the factors listed, and more to the point, they don't have the time. Some of the weights on these factors are unknown - is the reputational cost of offending this particular customer more or less than £1? - and therefore while head office might make an attempt to consider them, all that finds its way down to the staff level is a policy rule. If the decision is worth enough - let's say it is about a half-dozen bottles of Dom Perignon, which this bar sells at £99 each - then perhaps the manager will use their discretion - but below that, it's not even worth thinking about. And granularity implies that it's all-or-nothing - while the waitress might make a snap decision to accept or reject the half-price offer, it definitely isn't worth haggling to find the equilibrium on the curve between 50% and 100%.

Simply put, the waitress can't know the answer to these questions, and thinking about them probably impairs her effective waitressing. Therefore the bar is right to take the choice away from her.

The traditional view is that reason 9 is outside the domain of economics. Economic theory works best when dealing with continuous quantities and no (or low) transaction costs; and reason 9 is the typical escape clause for "why economic analysis doesn't apply in this situation". But cognitive-behavioural economics can take cognitive incentives into account, and find the optimal point where mental costs are balanced by gains.

Therefore, while it's irrational not to take into account all your preferences in making a decision, it may be rational to commit yourself not to do so.

Comments

In the U. S. there is another question. Many restaurants and bars charge their waiters and waitresses for mistakes. In such a case it may be worth the waitress's while to accept partial payment and make up the difference herself.

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